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Two-center overlap integrals, three dimensional adaptive integration, and prolate ellipsoidal coordinates. (English) Zbl 1404.65012
Summary: Numerical, adaptive algorithm evaluating the overlap integrals between the Numerical Type Orbitals (NTO) is presented. The described algorithm exploits the properties of the prolate ellipsoidal coordinates, which are the natural choice for two-center overlap integrals. The algorithm is designed for numerical atomic orbitals with the finite support. Since the cusp singularity of the atomic orbitals vanish in the prolate ellipsoidal coordinate system, the adaptive integration algorithm in \({\mathbb{R}^3}\) generates small number of subdivisions. The efficiency and reliability of the algorithm is demonstrated for the overlap integrals evaluated for the selected pairs of Slater Type Orbitals (STO).
65D30 Numerical integration
41A55 Approximate quadratures
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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